Question: Solve for $n$, $ -\dfrac{8}{12n - 12} = \dfrac{n - 3}{15n - 15} - \dfrac{2}{15n - 15} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $12n - 12$ $15n - 15$ and $15n - 15$ The common denominator is $60n - 60$ To get $60n - 60$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{8}{12n - 12} \times \dfrac{5}{5} = -\dfrac{40}{60n - 60} $ To get $60n - 60$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{n - 3}{15n - 15} \times \dfrac{4}{4} = \dfrac{4n - 12}{60n - 60} $ To get $60n - 60$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{2}{15n - 15} \times \dfrac{4}{4} = -\dfrac{8}{60n - 60} $ This give us: $ -\dfrac{40}{60n - 60} = \dfrac{4n - 12}{60n - 60} - \dfrac{8}{60n - 60} $ If we multiply both sides of the equation by $60n - 60$ , we get: $ -40 = 4n - 12 - 8$ $ -40 = 4n - 20$ $ -20 = 4n $ $ n = -5$